The pair dropped their first set to Radek Stepanek and Pavel Vizner 3-6, then rebounded with 6-3, 7-5, 6-4 wins in the next three sets.
"It's been a long time since either myself of Nikolay has played doubles, so it was more of a question of trying to remember how to play," Andreev admitted. "After losing the opening set, we were told by our captain (Shamil Tarpischev) just to relax, and that was exactly what we needed."
If the Russians win either of Sunday's scheduled reverse singles matches, they will qualify their fourth straight Davis Cup semifinal appearance against either Sweden or Argentina. The Swedes trail Argentina 2-1.
On Sunday, Andreev faces Tomas Berdych and Marat Safin meets Stepanek.
Russia, a two-time Davis Cup champion and last year's runner-up to the United States, has split eight all-time matchups against the Czechs, but has won the last two meetings.
Swim Week Miami Beach 2014 [PHOTOS]